A374443 Triangle read by rows: T(n, k) = rad(gcd(n, k)) if n, k > 0, T(0, 0) = 1, where rad = A007947 and gcd = A109004.

1, 1, 1, 2, 1, 2, 3, 1, 1, 3, 2, 1, 2, 1, 2, 5, 1, 1, 1, 1, 5, 6, 1, 2, 3, 2, 1, 6, 7, 1, 1, 1, 1, 1, 1, 7, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6

Offset: 0

Author

Peter Luschny and Michael De Vlieger, Jul 12 2024

Keywords

• nonn
• tabl

Examples

			Triangle starts:
  [ 0]  1;
  [ 1]  1, 1;
  [ 2]  2, 1, 2;
  [ 3]  3, 1, 1, 3;
  [ 4]  2, 1, 2, 1, 2;
  [ 5]  5, 1, 1, 1, 1, 5;
  [ 6]  6, 1, 2, 3, 2, 1, 6;
  [ 7]  7, 1, 1, 1, 1, 1, 1, 7;
  [ 8]  2, 1, 2, 1, 2, 1, 2, 1, 2;
  [ 9]  3, 1, 1, 3, 1, 1, 3, 1, 1, 3;
  [10] 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10;
  [11] 11, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 11;
		

Crossrefs

Variant: A374433.

Cf. A374442 (row sums), A007947, A109004.

Programs

Maple

rad := n -> ifelse(n = 0, 1, NumberTheory:-Radical(n)):
T := (n, k) -> rad(igcd(n, k)); seq(seq(T(n, k), k = 0..n), n = 0..11);

Mathematica

rad[n_] := If[n == 0, 1, Product[p, {p, Select[Divisors[n], PrimeQ]}]];
T[n_, k_] := rad[GCD[n, k]]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten

Python

from math import gcd, prod
from sympy.ntheory import primefactors
def T(n, k) -> int: return prod(primefactors(gcd(n, k)))
for n in range(16): print([T(n, k) for k in range(n+1)])  # Peter Luschny, Jun 22 2025